Finite element error estimates for Neumann boundary control problems on graded meshes

Article

DOI: 10.1007/s10589-011-9427-x

Cite this article as:
Apel, T., Pfefferer, J. & Rösch, A. Comput Optim Appl (2012) 52: 3. doi:10.1007/s10589-011-9427-x

Abstract

A specific elliptic linear-quadratic optimal control problem with Neumann boundary control is investigated. The control has to fulfil inequality constraints. The domain is assumed to be polygonal with reentrant corners. The asymptotic behaviour of two approaches to compute the optimal control is discussed. In the first the piecewise constant approximations of the optimal control are improved by a postprocessing step. In the second the control is not discretized; instead the first order optimality condition is used to determine an approximation of the optimal control. Although the quality of both approximations is in general affected by corner singularities a convergence order of 3/2 can be proven provided that the mesh is sufficiently graded.

Keywords

Linear-quadratic elliptic optimal control problem Boundary control A-priori error estimates Mesh grading Postprocessing Variational discretization 

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Universität der Bundeswehr MünchenNeubibergGermany
  2. 2.Universität Duisburg-EssenDuisburgGermany

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